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Mar 4, 2012, 7:27:05 AM3/4/12

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An experiment to perform in order to prove experimentally whether Pi

exists independently from the mind

exists independently from the mind

The idea came during discussion on embryophysics list

http://groups.google.com/group/embryophysics/t/419d3c1fec30e3b5

Below there is a description of the experiment that one could think of

to check the relationships between Mathematics, Mind and Nature (the MMN

experiment). In my view this could be done as a real experiment (so this

is actually not a thought experiment) provided we find two

mathematicians who agree to sacrifice their life for science. I believe

that this should be not that difficult provided the importance of the

experiment for the modern science.

Let us take a completely isolated bunker where the experiment begins.

The initial conditions are enough so that mathematicians can comfortably

chat for awhile with each other about Pi and prove that it exists.

Eventually the oxygen in the bunker will run over and both

mathematicians die. From a viewpoint of a natural science, we have a

dynamical system that eventually comes to the equilibrium state. I

assume that at the beginning when mathematicians prove that Pi exists we

have a consequence of physical states where Pi exists indeed. If you are

in doubt, please suggest any other physical states where you say that Pi

exists. The goal of the experiment is to establish what happens with Pi

at the end when the system reaches the stationary state.

Because of experimental settings, we can neglect the interaction with

environment and I hope that this could be done even for the quantum

mechanics treatment.

Before the experiment will be perform in real, you can take your bet on

whether Pi is retained after the death of mathematicians or not.

Mar 4, 2012, 8:39:13 AM3/4/12

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I confess I cannot make any sense of what you say here. What do you

mean by "Pi is retained", how do you verify this (after the death of

the mathematicians)?

Also, what is the initial theory that you have to use to interpret the

experience?

I have no clue of the meaning of "I assume that at the beginning when

mathematicians prove that Pi exists we have a consequence of physical

states where Pi exists indeed". "consequence of physical states where

Pi exists" contains too many vague abuse of languages.

When mathematicians proves that Pi exists, they assume a lot (real

numbers, circles, length of enough smooth curves, set theory, etc.).

Usually, they don't prove that Pi exist, they assume that all Cauchy

sequences define some number, called "real number", and they show that

curves sufficiently smooth have a length definable by such a sequence.

Then they define Pi, by the ratio of the length of a circle with its

diameter, and build the Cauchy sequence defining it.

And also, why those two poor mathematicians have to die? Is not Earth

close enough, and the death of Archimedes enough? (assuming the rest

makes sense).

You might just be joking, perhaps.

Bruno

Mar 4, 2012, 11:12:43 AM3/4/12

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Bruno,

Actually it is not a joke. I guess it is my first step toward Platonia.

As I am a chemist by background, the problem might be not mathematically

correct indeed. Yet, if you could help, we could improve it in this respect.

The background is as follows. I am a chemist and I am still at the level

of what you refer to as physicalism or mechanism. Before I consider your

theorem, first I would like to understand better in my own terms what

physicalsim and mechanism mean and what are the limits. When you talk

about this, it is too fast for me.

According to a common view in natural sciences, a human being (and hence

mind) has been created during evolution. Right now however, after

following discussion here, I have a problem with mathematics along this

way. Science has been pretty successful with mathematical models in

physics, chemistry and even in biology. Yet, according to my current

view, mathematics has been created by the mankind. Thereafter I have got

suddenly a question, why mathematical models (physical laws) are working

at all to describe the Universe when there was no mind. The mathematics,

it seems, was not there at the times of Big Bang.

We cannot repeat Big Bang to understand this. According to the current

economic situation, it is highly unlikely that taxpayers are ready to

spend money on bigger and bigger particle accelerators. Hence my

proposal. If we cannot repeat Big Bang, then for a relatively small

budget we could make easily a local heat death of a small Universe with

two mathematicians and see what happens with mathematics there. In a

way, we repeat evolution in the reverse direction.

It would be nice to exclude mind out of consideration at all but as this

is impossible my goal was to reduce its role as possible. We know that

mathematics is what mathematicians do. Pi is a nice number and most of

taxpayers have heard about it. In the experiment we could allow

mathematicians to write the prove that Pi exists on a paper, it would be

even simpler. If you think that some other mathematical object would be

nicer, please make your suggestion.

So, at the beginning of the experiment we have mind (two working brains

of mathematicians) and they prove on the paper that a given mathematical

object exists. An open question to discuss is what happens with this

mathematical object at the end of the experiment.

Evgenii

On 04.03.2012 14:39 Bruno Marchal said the following:

Mar 4, 2012, 11:28:07 AM3/4/12

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There is an important distinction between the names and notations of mathematics and the objects of study of mathematics. I believe the former are inventions of humans while the latter exist independently of mankind. For example, I am saying that the symbol 0 is an invention of mankind but what is pointed to by the symbol 0 is not an invention of mankind.

I can't give you absolute proof especially when we're going to assume different things (i.e., we live in different paradigms). One thing that gives me a clue about my conclusion is that mathematical objects will not exist any less if humanity were to go extinct. However, arguing that is like arguing for a particular answer to a koan.

I can't give you absolute proof especially when we're going to assume different things (i.e., we live in different paradigms). One thing that gives me a clue about my conclusion is that mathematical objects will not exist any less if humanity were to go extinct. However, arguing that is like arguing for a particular answer to a koan.

Mar 4, 2012, 12:48:53 PM3/4/12

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On 04 Mar 2012, at 17:12, Evgenii Rudnyi wrote:

> Bruno,

>

> Actually it is not a joke. I guess it is my first step toward

> Platonia. As I am a chemist by background, the problem might be not

> mathematically correct indeed. Yet, if you could help, we could

> improve it in this respect.

>

> The background is as follows. I am a chemist and I am still at the

> level of what you refer to as physicalism or mechanism.

Hmm... You should read more carefully the post. On the contrary I

claim, and explain, that mechanism and physicalism are incompatible.

I am aware that physicalist, naturalist and materialist tend to use

mechanism as a sort of modern way to put the mind under the rug.

You can see all what I am talking about as an explanation that not

only mechanism does not solve the mind-body problem, but on the

contrary, it leads to the falsity of physicalism and the necessity to

explain where the physical (and physicalist) *belief* come from.

Mechanism entails the negation of physicalism. That's what the UDA is

all about.

The physical reality is not the fundamental reality. The physical

reality will reappear as the way the border of the mathematical

reality looks when seen form inside, from some points of view

(actually the points of view of predicting measurement values).

I can argue that with comp, concerning the basic ontological level, it

is absolutely undecidable if there is anything more than the numbers,

that is 0, the successor of zero, the successor of the successor of

zero, ...

And every lawful thing is deducible from the laws of addition and

multiplication (that you have learn is school, and certainly apply in

chemistry).

So, with mechanism, physics is not the fundamental science. Physics

has to be reduced to digital machine (number) biology, psychology,

theology (given that non provable truth have a big role in the origin

of matter).

> Before I consider your theorem, first I would like to understand

> better in my own terms what physicalsim and mechanism mean and what

> are the limits. When you talk about this, it is too fast for me.

You have to do the thought experiment. You have to admit the

hypothesis, if only for the sake of the argument.

>

> According to a common view in natural sciences, a human being (and

> hence mind) has been created during evolution.

Something like that might be locally correct, but appears to be wrong

in the comp (digital mechanist) theory.

> Right now however, after following discussion here, I have a problem

> with mathematics along this way. Science has been pretty successful

> with mathematical models in physics, chemistry and even in biology.

> Yet, according to my current view, mathematics has been created by

> the mankind. Thereafter I have got suddenly a question, why

> mathematical models (physical laws) are working at all to describe

> the Universe when there was no mind. The mathematics, it seems, was

> not there at the times of Big Bang.

You might confuse mathematics, branch of human science, and the

possible mathematical reality.

The mathematical reality does not depend on the physical reality, and

a large part of it might no depend on the human mind.

For example the fact that 17 is prime, is a mathematical fact which

does not depend on the presence of human. It is just the fact that a

line of 17 distinguishable objects cannot be cut in a finite of part

to be reassembled into a rectangle different from the line itself. For

example 8 is not prime because the line

. . . . . . . .

can be cut and become

. . . .

. . . .

You might convince you experimentally that 17 is prime in this way,

but you can also prove it entirely as a consequence of the laws of

addition and multiplication. No concept of physics enter in this at

all. You might *apparently* need a physical reality to convince a

human being that 17 is prime, but you don't need to refer to it to

transmit the concept of prime number, despite it can helps for the

intuition, like above.

>

> We cannot repeat Big Bang to understand this.

Remember that we (try) to be scientist, meaning that we cannot commit

ourself ontologically, except by making clear our postulate. The big-

bang theory is a theory, an hypothesis, which usually assume an

ontological (primitively existing) universe.

With mechanism, that theory is already refuted by UDA+MGA.

What is the big bang, then. Open problem. Most plausibly a first

person plural sharable computational state of some universal number.

> According to the current economic situation, it is highly unlikely

> that taxpayers are ready to spend money on bigger and bigger

> particle accelerators. Hence my proposal. If we cannot repeat Big

> Bang, then for a relatively small budget we could make easily a

> local heat death of a small Universe with two mathematicians and see

> what happens with mathematics there. In a way, we repeat evolution

> in the reverse direction.

I can see you don't like mathematician!

:)

>

> It would be nice to exclude mind out of consideration at all but as

> this is impossible my goal was to reduce its role as possible. We

> know that mathematics is what mathematicians do.

Some constructivist mathematicians might agree, but most

mathematicians consider that they explore territories. They consider

that they make discoveries. Most discoveries are unexpected.

especially after Gödel, it is hard to defend a conventionalist

philosophy of math. And the, just to define what could mean

"mechanism", you need to assume that the arithmetical truth is more

primary than the mathematicians, if only to model mechanist

mathematicians by (Löbian) numbers. The you can distinguish the math

produce by the number, and the math of the number.

> Pi is a nice number

But it is a real number. I prefer to exclude them of the ontology,

because they have the same fate as matter. If they have an ontological

existence, it will not change anything in the machine (number)

epistemology. So they are like invisible horses, and with occam, you

can exclude them. Natural numbers will belief in real number,

independently of any of their ontological status.

> and most of taxpayers have heard about it. In the experiment we

> could allow mathematicians to write the prove that Pi exists on a

> paper, it would be even simpler. If you think that some other

> mathematical object would be nicer, please make your suggestion.

It is very weird, here.

>

> So, at the beginning of the experiment we have mind (two working

> brains of mathematicians) and they prove on the paper that a given

> mathematical object exists. An open question to discuss is what

> happens with this mathematical object at the end of the experiment.

Mathematical objects are invariant. Nothing happens to them. Things

can happen to them, in a relative sense, by the intermediate of true

relation bearing on them.

If you divide 8 by 4, this gives 2. But 8 remains untouched by that

operation. It is just that it is true that there exist a number which

multiplied by 4 gives 8, and that such a number is 2 (the nickname for

the successor of the successor of 0).

Mathematical object are structured only by their relations, and this

in a way which does not depend on time, space, animals, humans, or

whatever. Indeed, that is why math is useful to describe atemporally

even temporal relation, by a function of the type y = f(t).

But all questions require a precise theory in the background, and if

what I say don't help, you might think about formalizing a bit more

the background you are using.

Bruno

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Mar 4, 2012, 3:07:32 PM3/4/12

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I understand your logic but then immediately comes a question where

mathematics objects exist. In this case Bruno is consistent when he says

that everything is formed from the mathematical objects in Platonia. Do

you mean the same?

mathematics objects exist. In this case Bruno is consistent when he says

that everything is formed from the mathematical objects in Platonia. Do

you mean the same?

I personally still at the position that there are some material objects,

atoms, molecules, crystals, etc., that are independent from the mind. I

believe that this is quite a typical position for natural sciences. Then

it is hard to imagine how mathematical objects coexist with physical

objects. Some sort of dualism?

Evgenii

On 04.03.2012 17:28 Brian Tenneson said the following:

Mar 4, 2012, 6:17:25 PM3/4/12

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Hello, Evgenii, my fellow (former) chemist: I ended up after my 38 patents in (environmental-polymer) chemistry with an agnosticism, not 'believeing' in the atom (don't even mention 'molecules' or the macromolecules I created). It is all the figment of the human mind to EXPLAIN whatever transpired into our 'model' of presently knowables from (some?) infinite complexity - way beyond our imaginative power.

Maxim:

EVERYTHING **does** exist that pops up in the mind, if not otherwise: as an idea - in the mind. That is not too much help for your condition of "independently from the mind", but nothing we can 'think of' is independent from the mind. Pi is a formulatin of some effect humans found in the figment of their physical world explanations. The fact that we cannot express it in real numbers has nothing to do with its 'existence'. The 'effect did not evolve, it came with the "big Bang" (if you are a believer of it). Not with that 'retrograde history' of course, lineraly as it is drawn, reversing a postulated developmental course that is by far not 'linear'. Also: we have no proof that everything that ever showed up for us NOW is still available for us to know of.

Also it is childish to apply the mathematics of our expanded universe to the un-really concentrated energy-knot of the alleged beginning. (Physics as well). (Just think about the fairytale of the Inflation).

Please do not position your executable 2 scientists in the bunker before the human mind invented (discovered, as some would say) the zero. Or: writing.

Or: before the Great Greeks (Euclide, Plato, Archimedes, Aristotle etc.)

The 'setup' is by all means within my dismissal of 'thought experiments'.

IMO PI is a human formulation of something that is more than just human.

Regards

John

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Mar 5, 2012, 12:33:13 AM3/5/12

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On Mar 4, 3:07 pm, Evgenii Rudnyi <use...@rudnyi.ru> wrote:

>

> I personally still at the position that there are some material objects,

> atoms, molecules, crystals, etc., that are independent from the mind.

If you assume that the human mind is the only sense in the entire
>

> I personally still at the position that there are some material objects,

> atoms, molecules, crystals, etc., that are independent from the mind.

cosmos then there are going to be a lot of strange conclusions that

come up. Think about the hundreds of billions of galaxies...the

billions of organisms on this planet alone.. were all of them utterly

blind and deaf to their own existence for their entire history until

the moment that Homo sapiens began to take an interest in them from

their home on this remote speck of dust?

"Thereafter I have got suddenly a question, why mathematical models

(physical laws) are working at all to describe the Universe when there

was no mind. "

inertia. Worlds. The more intelligent you are, the more worlds you can

make sense of. The more you can make sense of the motivations and

processes of lesser worlds. As the collective intelligence of our

species has concentrated the knowledge available to each of us, we

gathered meta-perceptual commonalities. Mathematical models are

actually common perception/participation strategies as characterized

by ourselves as outside observers. We are made of matter, so we see

ourselves reflected in a particular way in matter. A way which is both

intimately familiar and alien to us.

The problem is that matter is only half of the story. We are also made

of ourselves. We need mathematical models to plumb the depths of

mysteries which are beyond our own frame of reference. Mysteries that

cut across distant levels like physics and chemistry. The closer we

get to our own level of perception however, the less mathematical

models tell the whole story. Biology, zoology, anthropology,

psychology, all benefit from mathematical models to some extent, but

they fall short of modeling what it is to be alive, to be a person,

etc. Mathematics is by definition an exterior facing manipulation. It

begins by counting on our fingers - an exterior computation which

transforms part of our body to a true set of objects - generic,

recursive, controllable. Our fingers are not a mind. They are the

beginnings of the mind offloading its grunt work onto objects. It is a

way of generalizing part of ourselves to make it seem like it is not

part of ourselves.'

Right now, in the post-Enlightenment era, our success with mathematics

has been so impressive that we have begun to imagine that we ourselves

have a mathematical basis. It is a little like following the counting

of the fingers back into the brain to find where smaller and smaller

fingers are counting. If we try a sense-based model instead, there is

no problem with mathematics being both a high level symbolic

experience within a human cortex as well as indirect experiences of

low level microcosmic events or other events which can be detected and

controlled externally with physical instruments. This is what sense

does. It jumps to conclusions. It ties levels together figuratively.

We want to move our hand, and we just do it. We don't have to

consciously transduce a signal through neural and muscular fibers. We

couldn't find a muscle fiber even if we wanted to.

This is what mathematics does for us, it extends our minds

figuratively outside of our native scale of perception, so that we

can, in a way, make more of the universe part of our figurative body.

Of course, just as we control our limbs without knowing what is really

going on under the skin, we should not mistake our success with

controlling through mathematical models for understanding the truth -

particularly the truth of our own native perceptual frame, which as

much more subtle and non-mathematical potentials. It could well be the

case that introducing our external control schemas into our own world

is having increasingly toxic consequences, draining the significance

out of culture and promoting an unstoppable drone of financial

computation which consumes the whole of civilization. We may find out

that our mastery over our universe has a Sorcerer's Apprentice side

which reduces itself to an automaton even as it automates everything

around it.

Craig

Mar 5, 2012, 6:23:21 AM3/5/12

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Bruno,

Thanks for your comments. You are right. It is necessary to be more

accurate with terms. I have read about physicalism on SEP and I see that

I do not need mechanism right now. By the way, where I can read about

mechanism? I see nothing on SEP.

Below is a new version of the problem. I have left Pi though.

Evgenii

P.S. I like a lot this quote about physicalism from SEP

"The first thing to say when considering the truth of physicalism is

that we live in an overwhelmingly physicalist or materialist

intellectual culture. The result is that, as things currently stand, the

standards of argumentation required to persuade someone of the truth of

physicalism are much lower than the standards required to persuade

someone of its negation. (The point here is a perfectly general one: if

you already believe or want something to be true, you are likely to

accept fairly low standards of argumentation for its truth.)"

I should confess that it describes my personal feeling very well. Cheers

to philosophers.

----------------------------------------------------------------

An experiment to perform in order to find experimentally what is the

meaning of Pi under the physicalism hypothesis

Version 2.0

*Assumptions*

-------------

I assume physicalism. From SEP

http://plato.stanford.edu/entries/physicalism/

"Physicalism is the thesis that everything is physical, or as

contemporary philosophers sometimes put it, that everything supervenes

on, or is necessitated by, the physical."

"The general idea is that the nature of the actual world (i.e. the

universe and everything in it) conforms to a certain condition, the

condition of being physical. Of course, physicalists don't deny that the

world might contain many items that at first glance don't seem physical

ï¿½ items of a biological, or psychological, or moral, or social nature.

But they insist nevertheless that at the end of the day such items are

either physical or supervene on the physical."

"Physicalism is sometimes known as ï¿½materialismï¿½; indeed, on one strand

to contemporary usage, the terms ï¿½physicalismï¿½ and ï¿½materialismï¿½ are

interchangeable."

*Problem*

---------

The Pi number enjoys extensive use in physics. This raises the question

what Pi means under the physicalism hypothesis.

*Experiment*

------------

Below there is a description of the experiment that one could think of

to check the relationships between Pi and physicalism.

Let us take a completely isolated bunker where the experiment begins.

There are two mathematicians in the bunker and the initial conditions

are enough so that mathematicians can comfortably work for awhile and

prove the existence of Pi on a paper. Eventually the oxygen in the

bunker will run over and both mathematicians die.

From a physicalism viewpoint, we have a dynamical system that

eventually comes to the equilibrium state. Because of experimental

settings, we can neglect the interaction with environment and I hope

that this could be done even for the quantum mechanics treatment.

The experiment takes an operational approach to what Pi means. During

the initial stage of the experiment mathematicians prove the existence

of Pi. This should be enough to claim that Pi is present in the bunker

at least for some moments.

*Questions to discuss*

----------------------

How Pi supervenes to the physical states of the bunker with mathematicians?

Is Pi invariant in respect to states of the dynamical system in question

or not?

On 04.03.2012 18:48 Bruno Marchal said the following:

> big-bang theory is a theory, an hypothesis, which usually assume an

> ontological (primitively existing) universe.

>

> With mechanism, that theory is already refuted by UDA+MGA.

>

> What is the big bang, then. Open problem. Most plausibly a first

> person plural sharable computational state of some universal number.

>

>

>

>

>

>> According to the current economic situation, it is highly unlikely

>> that taxpayers are ready to spend money on bigger and bigger

>> particle accelerators. Hence my proposal. If we cannot repeat Big

>> Bang, then for a relatively small budget we could make easily a

>> local heat death of a small Universe with two mathematicians and

>> see what happens with mathematics there. In a way, we repeat

>> evolution in the reverse direction.

>

> I can see you don't like mathematician! :)

>

>

>

>>

>> It would be nice to exclude mind out of consideration at all but as

>> this is impossible my goal was to reduce its role as possible. We

>> know that mathematics is what mathematicians do.

>

> Some constructivist mathematicians might agree, but most

> mathematicians consider that they explore territories. They consider

> that they make discoveries. Most discoveries are unexpected.

> especially after Gï¿½del, it is hard to defend a conventionalist

> philosophy of math. And the, just to define what could mean

> "mechanism", you need to assume that the arithmetical truth is more

> primary than the mathematicians, if only to model mechanist

> mathematicians by (Lï¿½bian) numbers. The you can distinguish the math

Mar 5, 2012, 7:01:44 AM3/5/12

to everyth...@googlegroups.com

John,

It is not that bad to say that we do not know something. Yet, it might

be even better to specify more accurately what exactly we do not know.

Think of your younger colleagues that do chemistry research right now.

Chemists have been quite successful and the story continues. The

concepts of atom, molecule, macromolecule, electron density, etc. have

helped a lot along this way. We may take this concepts ontologically or

just pragmatically, this is after all not that important. Materials

science seems not to be affected.

Evgenii

On 05.03.2012 00:17 John Mikes said the following:

> Hello, Evgenii, my fellow (former) chemist: I ended up after my 38

> patents in (environmental-polymer) chemistry with an agnosticism, not

> 'believeing' in the atom (don't even mention 'molecules' or the

> macromolecules I created). It is all the figment of the human mind to

> EXPLAIN whatever transpired into our 'model' of presently knowables

> from (some?) infinite complexity - way beyond our imaginative power.

> Maxim: EVERYTHING *does* exist that pops up in the mind, if not

Mar 5, 2012, 8:34:14 AM3/5/12

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Hi Evgenii,

This is a very fascinating statement to me and I find John's comments to be very wise! "...it might be even better to specify more accurately what exactly we do not know. " Does it not lead to a paradox? For if we could state exactly what we do not know then it would be the case that we do in fact know it and thus "we would known what we do not know", which appears to be a contradiction.

Is this a sample of a more general kind of situation that is inevitable given the idea of self-reference? It seems to me that we need to consider that Bivalency can be a source of error sometimes, or claim that knowledge is impossible. (note the bivalence here! LOL!) I am focusing on this because it it part of my overall critique of the idea of a Theory of Everything. For example, what exactly does it mean for a sentence to have a definite truth value absent the ability to evaluate that truth value? This is what I see your hypothetical situation as discussing....

Onward!

Stephen

This is a very fascinating statement to me and I find John's comments to be very wise! "...it might be even better to specify more accurately what exactly we do not know. " Does it not lead to a paradox? For if we could state exactly what we do not know then it would be the case that we do in fact know it and thus "we would known what we do not know", which appears to be a contradiction.

Is this a sample of a more general kind of situation that is inevitable given the idea of self-reference? It seems to me that we need to consider that Bivalency can be a source of error sometimes, or claim that knowledge is impossible. (note the bivalence here! LOL!) I am focusing on this because it it part of my overall critique of the idea of a Theory of Everything. For example, what exactly does it mean for a sentence to have a definite truth value absent the ability to evaluate that truth value? This is what I see your hypothetical situation as discussing....

Onward!

Stephen

Mar 5, 2012, 12:29:33 PM3/5/12

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On 3/5/2012 3:23 AM, Evgenii Rudnyi wrote:

The experiment takes an operational approach to what Pi means. During the initial stage of the experiment mathematicians prove the existence of Pi.

When mathematicians 'prove the existence' of something they are just showing that something which satisfies a certain definition can be inferred from a certain set of axioms.ï¿½ In your example the mathematicians may define Pi as the ratio of the circumference to the diameter of a circle in Euclidean geometry. But what does that mean if geometry is not Euclidean; and we know it's not since these mathematicians are in the gravitational field of the Earth.ï¿½ Mathematics is about abstract propositions.ï¿½ Whether they apply to reality is a separate question.

Brent

Mar 5, 2012, 1:03:26 PM3/5/12

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On 05.03.2012 18:29 meekerdb said the following:

> On 3/5/2012 3:23 AM, Evgenii Rudnyi wrote:

>> The experiment takes an operational approach to what Pi means.

>> During the initial stage of the experiment mathematicians prove the

>> existence of Pi.

>

> When mathematicians 'prove the existence' of something they are just

> showing that something which satisfies a certain definition can be

> inferred from a certain set of axioms. In your example the

> mathematicians may define Pi as the ratio of the circumference to the

> diameter of a circle in Euclidean geometry. But what does that mean

> if geometry is not Euclidean; and we know it's not since these

> mathematicians are in the gravitational field of the Earth.

> Mathematics is about abstract propositions. Whether they apply to

> reality is a separate question.

>

> Brent

>

>

> On 3/5/2012 3:23 AM, Evgenii Rudnyi wrote:

>> The experiment takes an operational approach to what Pi means.

>> During the initial stage of the experiment mathematicians prove the

>> existence of Pi.

>

> When mathematicians 'prove the existence' of something they are just

> showing that something which satisfies a certain definition can be

> mathematicians may define Pi as the ratio of the circumference to the

> diameter of a circle in Euclidean geometry. But what does that mean

> if geometry is not Euclidean; and we know it's not since these

> mathematicians are in the gravitational field of the Earth.

> reality is a separate question.

>

> Brent

>

>

I agree that this assumption might not be the best one. I will think it

over.

However, I do not completely understand you. How the geometry of

physical space in which mathematicians reside influences the definition

of Pi? Mathematicians will consider just Euclidean geometry, that's it.

In my view, whether the physical space Euclidean or not, does not

influence the work of mathematicians.

In any case, the problem remains. What is mathematics under the

assumption of physicalism? Do you have any idea?

Evgenii

Mar 5, 2012, 1:26:55 PM3/5/12

to everyth...@googlegroups.com

Exactly. Hence mathematics =/= reality.

>

> In any case, the problem remains. What is mathematics under the assumption of

> physicalism? Do you have any idea?

It's a language game.

Brent

A physicist goes off to a conference. After a week his suitï¿½s gotten soiled and crumpled,

so he goes out to look for a dry cleaner. Walking down the main street of town, he comes

upon a store with a lot of signs out front. One of them says ï¿½Dry Cleaning.ï¿½ So he goes in

with his dirty suit and asks when he can come back to pick it up. The mathematician who

owns the shop replies, ï¿½Iï¿½m terribly sorry, but we donï¿½t do dry cleaning.ï¿½ ï¿½What?ï¿½

exclaims the puzzled physicist. ï¿½The sign outside says ï¿½Dry Cleaningï¿½!ï¿½ ï¿½We do not do

anything here,ï¿½ replies the mathematician. ï¿½We only sell signs!ï¿½

--- Alain Connes, in Changeux

>

> Evgenii

>

Mar 5, 2012, 7:57:18 PM3/5/12

to everyth...@googlegroups.com

On Mon, Mar 5, 2012 at 12:26 PM, meekerdb <meek...@verizon.net> wrote:

On 3/5/2012 10:03 AM, Evgenii Rudnyi wrote:Exactly. Hence mathematics =/= reality.

On 05.03.2012 18:29 meekerdb said the following:

On 3/5/2012 3:23 AM, Evgenii Rudnyi wrote:

The experiment takes an operational approach to what Pi means.

During the initial stage of the experiment mathematicians prove the

existence of Pi.

When mathematicians 'prove the existence' of something they are just

showing that something which satisfies a certain definition can be

inferred from a certain set of axioms. In your example the

mathematicians may define Pi as the ratio of the circumference to the

diameter of a circle in Euclidean geometry. But what does that mean

if geometry is not Euclidean; and we know it's not since these

mathematicians are in the gravitational field of the Earth.

Mathematics is about abstract propositions. Whether they apply to

reality is a separate question.

Brent

I agree that this assumption might not be the best one. I will think it over.

However, I do not completely understand you. How the geometry of physical space in which mathematicians reside influences the definition of Pi? Mathematicians will consider just Euclidean geometry, that's it. In my view, whether the physical space Euclidean or not, does not influence the work of mathematicians.

This is like comparing the kidney of a whale to a liver of a whale, and deciding whale=/=whale. You can't compare one limited subset of the whole (such as the local part of this universe) with another subset of the whole (euclidean geometry), and decide that the whole (of mathematics) is different from the whole (of reality).

It's a language game.

In any case, the problem remains. What is mathematics under the assumption of physicalism? Do you have any idea?

This is what Hilbert proposed and what others such as Bertrand Russel tried to prove, but instead the opposite was proved in 1931. Mathematical truth transcends the symbol manipulation game defined by any set of axioms.

Jason

Brent

A physicist goes off to a conference. After a week his suit’s gotten soiled and crumpled, so he goes out to look for a dry cleaner. Walking down the main street of town, he comes upon a store with a lot of signs out front. One of them says “Dry Cleaning.” So he goes in with his dirty suit and asks when he can come back to pick it up. The mathematician who owns the shop replies, “I’m terribly sorry, but we don’t do dry cleaning.” “What?” exclaims the puzzled physicist. “The sign outside says ‘Dry Cleaning’!” “We do not do anything here,” replies the mathematician. “We only sell signs!”

--- Alain Connes, in Changeux

Evgenii

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Mar 5, 2012, 8:24:00 PM3/5/12

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On 3/5/2012 4:57 PM, Jason Resch wrote:

On Mon, Mar 5, 2012 at 12:26 PM, meekerdb <meek...@verizon.net> wrote:

On 3/5/2012 10:03 AM, Evgenii Rudnyi wrote:Exactly. Hence mathematics =/= reality.

On 05.03.2012 18:29 meekerdb said the following:

On 3/5/2012 3:23 AM, Evgenii Rudnyi wrote:

The experiment takes an operational approach to what Pi means.

During the initial stage of the experiment mathematicians prove the

existence of Pi.

When mathematicians 'prove the existence' of something they are just

showing that something which satisfies a certain definition can be

inferred from a certain set of axioms. In your example the

mathematicians may define Pi as the ratio of the circumference to the

diameter of a circle in Euclidean geometry. But what does that mean

if geometry is not Euclidean; and we know it's not since these

mathematicians are in the gravitational field of the Earth.

Mathematics is about abstract propositions. Whether they apply to

reality is a separate question.

Brent

I agree that this assumption might not be the best one. I will think it over.

However, I do not completely understand you. How the geometry of physical space in which mathematicians reside influences the definition of Pi? Mathematicians will consider just Euclidean geometry, that's it. In my view, whether the physical space Euclidean or not, does not influence the work of mathematicians.

This is like comparing the kidney of a whale to a liver of a whale, and deciding whale=/=whale. ï¿½You can't compare one limited subset of the whole (such as the local part of this universe) with another subset of the whole (euclidean geometry), and decide that the whole (of mathematics) is different from the whole (of reality).

The same mathematicians in the same place could 'prove the existence' of the meeting point of parallel lines or that through a point there is more than one line parallel to a given line.ï¿½ So no matter what they measure in their bunker it will be consistent with one or the other.ï¿½ So you can only hold that mathematics=reality if you assume everything not self-contradictory exists in reality; but that was what the bunker thought experiment was intended to test.ï¿½ You've essentially made it untestable by saying, well it may fail HERE but somewhere (Platonia?) it's really true.

Brent

ï¿½

It's a language game.

In any case, the problem remains. What is mathematics under the assumption of physicalism? Do you have any idea?

This is what Hilbert proposed and what others such as Bertrand Russel tried to prove, but instead the opposite was proved in 1931. ï¿½Mathematical truthï¿½transcends theï¿½symbol manipulation game defined by any set of axioms.

Jasonï¿½Brent

A physicist goes off to a conference. After a week his suitï¿½s gotten soiled and crumpled, so he goes out to look for a dry cleaner. Walking down the main street of town, he comes upon a store with a lot of signs out front. One of them says ï¿½Dry Cleaning.ï¿½ So he goes in with his dirty suit and asks when he can come back to pick it up. The mathematician who owns the shop replies, ï¿½Iï¿½m terribly sorry, but we donï¿½t do dry cleaning.ï¿½ ï¿½What?ï¿½ exclaims the puzzled physicist. ï¿½The sign outside says ï¿½Dry Cleaningï¿½!ï¿½ ï¿½We do not do anything here,ï¿½ replies the mathematician. ï¿½We only sell signs!ï¿½

--- Alain Connes, in Changeux

Evgenii

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Mar 5, 2012, 11:28:33 PM3/5/12

to everyth...@googlegroups.com

On Mon, Mar 5, 2012 at 7:24 PM, meekerdb <meek...@verizon.net> wrote:

On 3/5/2012 4:57 PM, Jason Resch wrote:

On Mon, Mar 5, 2012 at 12:26 PM, meekerdb <meek...@verizon.net> wrote:

On 3/5/2012 10:03 AM, Evgenii Rudnyi wrote:Exactly. Hence mathematics =/= reality.

On 05.03.2012 18:29 meekerdb said the following:

On 3/5/2012 3:23 AM, Evgenii Rudnyi wrote:

During the initial stage of the experiment mathematicians prove the

existence of Pi.

When mathematicians 'prove the existence' of something they are just

showing that something which satisfies a certain definition can be

inferred from a certain set of axioms. In your example the

mathematicians may define Pi as the ratio of the circumference to the

diameter of a circle in Euclidean geometry. But what does that mean

if geometry is not Euclidean; and we know it's not since these

mathematicians are in the gravitational field of the Earth.

Mathematics is about abstract propositions. Whether they apply to

reality is a separate question.

Brent

I agree that this assumption might not be the best one. I will think it over.

However, I do not completely understand you. How the geometry of physical space in which mathematicians reside influences the definition of Pi? Mathematicians will consider just Euclidean geometry, that's it. In my view, whether the physical space Euclidean or not, does not influence the work of mathematicians.

The same mathematicians in the same place could 'prove the existence' of the meeting point of parallel lines or that through a point there is more than one line parallel to a given line. So no matter what they measure in their bunker it will be consistent with one or the other. So you can only hold that mathematics=reality if you assume everything not self-contradictory exists in reality;This is like comparing the kidney of a whale to a liver of a whale, and deciding whale=/=whale. You can't compare one limited subset of the whole (such as the local part of this universe) with another subset of the whole (euclidean geometry), and decide that the whole (of mathematics) is different from the whole (of reality).

Okay.

but that was what the bunker thought experiment was intended to test.

I fail to see how the bunker experiment tests this. The bunker experiment seems to assume that mathematical reality is or depends upon a physical representation.

You've essentially made it untestable by saying, well it may fail HERE but somewhere (Platonia?) it's really true.

People used to say Darwin's theory was untestable, because evolution was such a slow process they thought it could never be observed. Some on this list have argued that the hypothesis has already survived one test: the unpredictability in quantum mechanics. If instead we found our environment and observations of it to be perfectly deterministic, this would have ruled out mechanism+a single or finite universe. Further, there is a growing collection of evidence that in most universes, conscious life is impossible. This can also be considered as confirmation of the theory that there exists a huge diversity in structures that have existence. Just because one proposed test will not work should not imply a theory is untestable.

A final thought: Consider what our universe would look like if you were a being outside it. You would not be affected by the gravity of objects in our universe, for gravity only affects physical objects in this universe. You could not see the stars or galaxies of our universe, for photons never leave it. There would be no relativity of size, or time, or distance between your perspective and that within our universe. You could not say what time it happened to be in our universe, or whether the world had even formed yet or long ago ended. You could in no way make your presence known to us in this universe, for our universe is bound to follow certain fixed laws. In summary, outside our universe there is no evidence we even exist; our entire universe is merely an abstract, immutable and timeless mathematical object. From the outside, one could study our universe through the window of math and computer simulation, but observation through your senses or any measurement apparatus would never reveal its existence.

Jason

Brent

It's a language game.

In any case, the problem remains. What is mathematics under the assumption of physicalism? Do you have any idea?

This is what Hilbert proposed and what others such as Bertrand Russel tried to prove, but instead the opposite was proved in 1931. Mathematical truth transcends the symbol manipulation game defined by any set of axioms.

JasonBrent

A physicist goes off to a conference. After a week his suit’s gotten soiled and crumpled, so he goes out to look for a dry cleaner. Walking down the main street of town, he comes upon a store with a lot of signs out front. One of them says “Dry Cleaning.” So he goes in with his dirty suit and asks when he can come back to pick it up. The mathematician who owns the shop replies, “I’m terribly sorry, but we don’t do dry cleaning.” “What?” exclaims the puzzled physicist. “The sign outside says ‘Dry Cleaning’!” “We do not do anything here,” replies the mathematician. “We only sell signs!”

--- Alain Connes, in Changeux

Evgenii

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No virus found in this message.

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Mar 5, 2012, 11:42:27 PM3/5/12

to everyth...@googlegroups.com

On 3/5/2012 8:28 PM, Jason Resch wrote:

On Mon, Mar 5, 2012 at 7:24 PM, meekerdb <meek...@verizon.net> wrote:

On 3/5/2012 4:57 PM, Jason Resch wrote:

During the initial stage of the experiment mathematicians prove the

existence of Pi.

When mathematicians 'prove the existence' of something they are just

showing that something which satisfies a certain definition can be

inferred from a certain set of axioms. In your example the

mathematicians may define Pi as the ratio of the circumference to the

diameter of a circle in Euclidean geometry. But what does that mean

if geometry is not Euclidean; and we know it's not since these

mathematicians are in the gravitational field of the Earth.

Mathematics is about abstract propositions. Whether they apply to

reality is a separate question.

Brent

I agree that this assumption might not be the best one. I will think it over.

However, I do not completely understand you. How the geometry of physical space in which mathematicians reside influences the definition of Pi? Mathematicians will consider just Euclidean geometry, that's it. In my view, whether the physical space Euclidean or not, does not influence the work of mathematicians.

The same mathematicians in the same place could 'prove the existence' of the meeting point of parallel lines or that through a point there is more than one line parallel to a given line.ï¿½ So no matter what they measure in their bunker it will be consistent with one or the other.ï¿½ So you can only hold that mathematics=reality if you assume everything not self-contradictory exists in reality;This is like comparing the kidney of a whale to a liver of a whale, and deciding whale=/=whale. ï¿½You can't compare one limited subset of the whole (such as the local part of this universe) with another subset of the whole (euclidean geometry), and decide that the whole (of mathematics) is different from the whole (of reality).

Okay.

ï¿½but that was what the bunker thought experiment was intended to test.ï¿½

I fail to see how the bunker experiment tests this.ï¿½ The bunker experiment seems to assume that mathematical reality is or depends upon a physical representation.

ï¿½

You've essentially made it untestable by saying, well it may fail HERE but somewhere (Platonia?) it's really true.

People used to say Darwin's theory was untestable, because evolution was such a slow process they thought it could never be observed.ï¿½ Some on this list have argued that the hypothesis has already survived one test: the unpredictability in quantum mechanics.ï¿½

That specific retrodiction came from Bruno's hypothesis which is that universes are generated by computation.ï¿½ What is computable is much less than all mathematics.

If instead we found our environment and observations of it to be perfectly deterministic, this would have ruled out mechanism+a single or finite universe.ï¿½ Further, there is a growing collection of evidence that in most universes, conscious life is impossible.

There's a popular idea that most possible universes are inhospitable to conscious life: a theory that might well be false under Bruno's hypothesis in which consciousness and universes are both realized by computation.ï¿½ In any case it doesn't warrant the conclusion that all possible universes exist.

ï¿½ This can also be considered as confirmation of the theory that there exists a huge diversity in structures that have existence.ï¿½ Just because one proposed test will not work should not imply a theory is untestable.

A final thought: Consider what our universe would look like if you were a being outside it.ï¿½ You would not be affected by the gravity of objects in our universe, for gravity only affects physical objects in this universe.ï¿½ You could not see the stars or galaxies of our universe, for photons never leave it.ï¿½ There would be no relativity of size, or time, or distance between your perspective and that within our universe.ï¿½ You could not say what time it happened to be in our universe, or whether the world had even formed yet or long ago ended.ï¿½ You could in no way make your presence known to us in this universe, for our universe is bound to follow certain fixed laws.ï¿½ In summary, outside our universe there is no evidence we even exist; our entire universe is merely an abstract, immutable and timeless mathematical object.

That's a complete non sequitur.

ï¿½ From the outside, one could study our universe through the window of math and computer simulation,

I could study a mathematical or computational representation, but that's not the same as studying our universe - unless you beg the question.

Brent

Mar 6, 2012, 12:34:05 AM3/6/12

to everyth...@googlegroups.com

On Mon, Mar 5, 2012 at 10:42 PM, meekerdb <meek...@verizon.net> wrote:

On 3/5/2012 8:28 PM, Jason Resch wrote:

On Mon, Mar 5, 2012 at 7:24 PM, meekerdb <meek...@verizon.net> wrote:

On 3/5/2012 4:57 PM, Jason Resch wrote:

During the initial stage of the experiment mathematicians prove the

existence of Pi.

When mathematicians 'prove the existence' of something they are just

showing that something which satisfies a certain definition can be

inferred from a certain set of axioms. In your example the

mathematicians may define Pi as the ratio of the circumference to the

diameter of a circle in Euclidean geometry. But what does that mean

if geometry is not Euclidean; and we know it's not since these

mathematicians are in the gravitational field of the Earth.

Mathematics is about abstract propositions. Whether they apply to

reality is a separate question.

Brent

I agree that this assumption might not be the best one. I will think it over.

However, I do not completely understand you. How the geometry of physical space in which mathematicians reside influences the definition of Pi? Mathematicians will consider just Euclidean geometry, that's it. In my view, whether the physical space Euclidean or not, does not influence the work of mathematicians.

The same mathematicians in the same place could 'prove the existence' of the meeting point of parallel lines or that through a point there is more than one line parallel to a given line. So no matter what they measure in their bunker it will be consistent with one or the other. So you can only hold that mathematics=reality if you assume everything not self-contradictory exists in reality;This is like comparing the kidney of a whale to a liver of a whale, and deciding whale=/=whale. You can't compare one limited subset of the whole (such as the local part of this universe) with another subset of the whole (euclidean geometry), and decide that the whole (of mathematics) is different from the whole (of reality).

Okay.

but that was what the bunker thought experiment was intended to test.

I fail to see how the bunker experiment tests this. The bunker experiment seems to assume that mathematical reality is or depends upon a physical representation.

You've essentially made it untestable by saying, well it may fail HERE but somewhere (Platonia?) it's really true.

That specific retrodiction came from Bruno's hypothesis which is that universes are generated by computation. What is computable is much less than all mathematics.

People used to say Darwin's theory was untestable, because evolution was such a slow process they thought it could never be observed. Some on this list have argued that the hypothesis has already survived one test: the unpredictability in quantum mechanics.

The existence of all mathematical structures implies the existence of all programs, which is observationally indistinguishable from Bruno's result taking only the integers to exist. I find the existence of all consistent structures to be a simpler theory. If the integers can exist, why cant the Mandlebrot set, or the Calabi–Yau manifolds?

If instead we found our environment and observations of it to be perfectly deterministic, this would have ruled out mechanism+a single or finite universe. Further, there is a growing collection of evidence that in most universes, conscious life is impossible.

There's a popular idea that most possible universes are inhospitable to conscious life: a theory that might well be false under Bruno's hypothesis in which consciousness and universes are both realized by computation.

In Bruno's theory, "physical universes" are considered observations of minds. Where I use the term, I refer to independent structures (both seen and unseen).

In any case it doesn't warrant the conclusion that all possible universes exist.

No, it doesn't prove they all exist, just that there are perhaps infinitely many universes almost exactly like this one. Which, while not proving everything exists, is certainly something we would expect to find if indeed everything exists.

There are all these reasons and arguments that are compatible with and suggestive of the idea that all is out there. I haven't seen one offered piece of evidence from you that would suggest the idea of mathematical reality is false. So tell me: for what reason(s) do you reject the hypothesis?

This can also be considered as confirmation of the theory that there exists a huge diversity in structures that have existence. Just because one proposed test will not work should not imply a theory is untestable.

A final thought: Consider what our universe would look like if you were a being outside it. You would not be affected by the gravity of objects in our universe, for gravity only affects physical objects in this universe. You could not see the stars or galaxies of our universe, for photons never leave it. There would be no relativity of size, or time, or distance between your perspective and that within our universe. You could not say what time it happened to be in our universe, or whether the world had even formed yet or long ago ended. You could in no way make your presence known to us in this universe, for our universe is bound to follow certain fixed laws. In summary, outside our universe there is no evidence we even exist; our entire universe is merely an abstract, immutable and timeless mathematical object.

That's a complete non sequitur.

From the outside, one could study our universe through the window of math and computer simulation,

I could study a mathematical or computational representation, but that's not the same as studying our universe - unless you beg the question.

Clearly we will not get proof of the mathematical universe hypothesis by seeing other universes and mathematical objects through telescopes. Different universes are independent in such a way that we can only access them as we access all other mathematical structures. Also, if your model is perfect, there should be no difference between studying the model and the object it represents. In the future, we will be able to discover, emulate, and visit other universes by discovering them in math, and using sufficiently powerful simulations, know what it is like there, or whether or not life is possible.

That we cannot affect them from our current location does not make them any less real. That our universe is an immutable, abstract, timeless object to a being in a different universe does not imply we are any less real, that our experiences don't matter, or that the existence of the structure that is our universe is without consequence. Immutability says nothing about an objects reality; we cannot affect the past, or portions of our universe sufficiently far away, yet most would say these exist. Moreover, that other universes are currently inaccessible to us does not necessarily imply that they will always be immutable and inaccessible to us. There is always some non-zero possibility that when you wake up tomorrow, you won't find yourself in this universe, but one very far away. The existence of all structures reconfirms, in a stronger senses, quantum immortality. If all the other universes are out there, then given mechanism, a we are all immortal. Unlike the immortality implied by quantum immortality, we can even survive destruction of this universe, waking up in a different one where the present one was just a very long dream.

Jason

Brent

Mar 6, 2012, 1:59:57 AM3/6/12

to everyth...@googlegroups.com

The same mathematicians in the same place could 'prove the existence' of the meeting point of parallel lines or that through a point there is more than one line parallel to a given line.ï¿½ So no matter what they measure in their bunker it will be consistent with one or the other.ï¿½ So you can only hold that mathematics=reality if you assume everything not self-contradictory exists in reality;This is like comparing the kidney of a whale to a liver of a whale, and deciding whale=/=whale. ï¿½You can't compare one limited subset of the whole (such as the local part of this universe) with another subset of the whole (euclidean geometry), and decide that the whole (of mathematics) is different from the whole (of reality).

Okay.

ï¿½but that was what the bunker thought experiment was intended to test.ï¿½

I fail to see how the bunker experiment tests this.ï¿½ The bunker experiment seems to assume that mathematical reality is or depends upon a physical representation.

ï¿½

That specific retrodiction came from Bruno's hypothesis which is that universes are generated by computation.ï¿½ What is computable is much less than all mathematics.

People used to say Darwin's theory was untestable, because evolution was such a slow process they thought it could never be observed.ï¿½ Some on this list have argued that the hypothesis has already survived one test: the unpredictability in quantum mechanics.ï¿½

The existence of all mathematical structures implies the existence of all programs, which is observationally indistinguishable from Bruno's result taking only the integers to exist.ï¿½

That they are observationally indistinguishable is vacuously satisfied by them both being unobservable.

I find the existence of all consistent structures to be a simpler theory.ï¿½ If the integers can exist, why cant the Mandlebrot set, or the Calabiï¿½Yau manifolds?

I didn't say that things descriable by those mathematics *can't* exist.ï¿½ I just said I don't believe they do.ï¿½ Yaweh *could* exist (and according to you does) but I don't believe he does.

ï¿½There's a popular idea that most possible universes are inhospitable to conscious life: a theory that might well be false under Bruno's hypothesis in which consciousness and universes are both realized by computation.ï¿½

If instead we found our environment and observations of it to be perfectly deterministic, this would have ruled out mechanism+a single or finite universe.ï¿½ Further, there is a growing collection of evidence that in most universes, conscious life is impossible.

In Bruno's theory, "physical universes" are considered observations of minds.ï¿½

Hmm? Is that right?ï¿½ The UD* certainly must generate lots of programs without human-like consciousness, e.g. this universe in which dinosaurs weren't killed off.ï¿½ So I'm not clear on why there wouldn't be infinitely many universes without conscious beings.

Where I use the term, I refer to independent structures (both seen and unseen).

ï¿½

In any case it doesn't warrant the conclusion that all possible universes exist.

No, it doesn't prove they all exist, just that there are perhaps infinitely many universes almost exactly like this one.ï¿½

Maybe I'm not understanding what you mean by "independent structures".ï¿½ Independent of what?ï¿½ I don't see that referring to independent structures has anything to do with whether they exist.

Which, while not proving everything exists, is certainly something we would expect to find if indeed everything exists.

Of course it is trivial to say that an everything theory
successfully predicts the existence of what we observe to exist.ï¿½
The question is whether it does the converse.ï¿½ Can it predict that
we don't see some (almost all) things.

I don't reject it; I just don't accept it.ï¿½ It seems to ill defined to be testable.

There are all these reasons and arguments that are compatible with and suggestive of the idea that all is out there.ï¿½ I haven't seen one offered piece of evidence from you that would suggest the idea of mathematical reality is false.ï¿½ So tell me: for what reason(s) do you reject the hypothesis?

I don't reject it; I just don't accept it.ï¿½ It seems to ill defined to be testable.

ï¿½

ï¿½ This can also be considered as confirmation of the theory that there exists a huge diversity in structures that have existence.ï¿½ Just because one proposed test will not work should not imply a theory is untestable.

A final thought: Consider what our universe would look like if you were a being outside it.ï¿½ You would not be affected by the gravity of objects in our universe, for gravity only affects physical objects in this universe.ï¿½ You could not see the stars or galaxies of our universe, for photons never leave it.ï¿½ There would be no relativity of size, or time, or distance between your perspective and that within our universe.ï¿½ You could not say what time it happened to be in our universe, or whether the world had even formed yet or long ago ended.ï¿½ You could in no way make your presence known to us in this universe, for our universe is bound to follow certain fixed laws.ï¿½ In summary, outside our universe there is no evidence we even exist; our entire universe is merely an abstract, immutable and timeless mathematical object.

That's a complete non sequitur.

ï¿½ From the outside, one could study our universe through the window of math and computer simulation,

I could study a mathematical or computational representation, but that's not the same as studying our universe - unless you beg the question.

Clearly we will not get proof of the mathematical universe hypothesis by seeing other universes and mathematical objects through telescopes.ï¿½ Different universes are independent in such a way that we can only access them as we access all other mathematical structures.ï¿½

Ask yourself WHY they are inaccessible.ï¿½ Isn't it because if they were accessible then there would be contradictory facts in the world.ï¿½ And why can't there be contradictory facts?ï¿½ Because ex falso quodlibet.ï¿½ But "quodlibet" is what has already been hypothesized. (on the other hand see Graham Priest's "In Contradiction").

Also, if your model is perfect, there should be no difference between studying the model and the object it represents.ï¿½ In the future, we will be able to discover, emulate, and visit other universes by discovering them in math, and using sufficiently powerful simulations, know what it is like there, or whether or not life is possible.

Except if we are studying them or simulating them, then we can interact with them and (necessarily?) change them.

That we cannot affect them from our current location does not make them any less real.ï¿½

"Affect" and "observe" are two different things (at least classically) and if we can neither affect or observe that makes them rather like Russell's teapot.ï¿½ We can't be sure it doesn't exist, but there's no reason to think it does.

That our universe is an immutable, abstract, timeless object to a being in a different universe does not imply we are any less real,

I'm not sure what being "an abstract object to a being" means, but I
don't think it implies we are any more real.

Unless the past was identical with the present then something has mutated.

So you say, but I'm betting not...and so are you.

I'm not sure I've survived the past year.

Brent

The person I was when I was 3 years old is dead. He died because

too much new information was added to his brain.

ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ -- Saibal Mitra

that our experiences don't matter, or that the existence of the structure that is our universe is without consequence.ï¿½ Immutability says nothing about an objects reality; we cannot affect the past,

Unless the past was identical with the present then something has mutated.

or portions of our universe sufficiently far away, yet most would say these exist.ï¿½ Moreover, that other universes are currently inaccessible to us does not necessarily imply that they will always be immutable and inaccessible to us.ï¿½ There is always some non-zero possibility that when you wake up tomorrow, you won't find yourself in this universe, but one very far away.

So you say, but I'm betting not...and so are you.

The existence of all structures reconfirms, in a stronger senses, quantum immortality.ï¿½ If all the other universes are out there, then given mechanism, a we are all immortal.ï¿½ Unlike the immortality implied by quantum immortality, we can even survive destruction of this universe, waking up in a different one where the present one was just a very long dream.

I'm not sure I've survived the past year.

Brent

The person I was when I was 3 years old is dead. He died because

too much new information was added to his brain.

ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ -- Saibal Mitra

Mar 6, 2012, 2:43:20 AM3/6/12

to everyth...@googlegroups.com

>>>> whole

>>>> (such as the local part of this universe) with another subset of the

>>>> whole

>>>> (euclidean geometry), and decide that the whole (of mathematics) is

>>>> different

>>>> from the whole (of reality).

>>>

>>> The same mathematicians in the same place could 'prove the existence'

>>> of the

>>> meeting point of parallel lines or that through a point there is more

>>> than one

>>> their bunker

>>> it will be consistent with one or the other. So you can only hold that

>>> mathematics=reality if you assume everything not self-contradictory

>>> exists in

>>> reality;

>>>

>>>

>>> Okay.

>>>

>>> but that was what the bunker thought experiment was intended to test.

>>>

>>>

>>> I fail to see how the bunker experiment tests this. The bunker>>>

>>>

>>> experiment seems to

>>> assume that mathematical reality is or depends upon a physical

>>> representation.

>>>

>>> You've essentially made it untestable by saying, well it may fail

>>> HERE but

>>> somewhere (Platonia?) it's really true.

>>>

>>>

>>> People used to say Darwin's theory was untestable, because evolution

>>> was such a

>>> slow process they thought it could never be observed. Some on this>>> HERE but

>>> somewhere (Platonia?) it's really true.

>>>

>>>

>>> People used to say Darwin's theory was untestable, because evolution

>>> was such a

>>> list have

>>> argued that the hypothesis has already survived one test: the

>>> unpredictability in

>>> quantum mechanics.

>>

>> That specific retrodiction came from Bruno's hypothesis which is that

>> universes are

>> generated by computation. What is computable is much less than all>> universes are

>> mathematics.

>>

>>

>> The existence of all mathematical structures implies the existence of

>> all programs, which is observationally indistinguishable from Bruno's

>> result taking only the integers to exist.

>

> That they are observationally indistinguishable is vacuously satisfied

> by them both being unobservable.

>

>> I find the existence of all consistent structures to be a simpler

>> theory. If the integers can exist, why cant the Mandlebrot set, or the> by them both being unobservable.

>

>> I find the existence of all consistent structures to be a simpler

>> Calabiï¿½Yau manifolds?

>

> I didn't say that things descriable by those mathematics *can't* exist.

> to you does) but I don't believe he does.

>

contradictory properties is a strawman.

>>

>>

>>> If instead we found our environment and observations of it to be

>>> perfectly

>>> deterministic, this would have ruled out mechanism+a single or finite

>>> most universes,

>>> conscious life is impossible.

>>

>> There's a popular idea that most possible universes are inhospitable

>> to conscious

>> life: a theory that might well be false under Bruno's hypothesis in which

>> consciousness and universes are both realized by computation.

>>

>>

>> In Bruno's theory, "physical universes" are considered observations of

>> minds.

>

> Hmm? Is that right? The UD* certainly must generate lots of programs>> minds.

>

> without human-like consciousness, e.g. this universe in which dinosaurs

> many universes without conscious beings.

>

>

like in-a-moment experience with very few memories or continuity.

Consciousness should not be confused with

self-awareness/self-consciousness. A mathematical object with no

conscious observer has no one to see it from the inside, thus it's

merely abstract (but for a mathematical monist or a non-eliminitavist

computationalist that would just be a program or structure empty of

observers). Of course, said structure could also find itself studied by

mathematicians, or simulated on computers or merely within other

structures (such as observer physical objects).

>> Where I use the term, I refer to independent structures (both seen and

>> unseen).

>>

>> In any case it doesn't warrant the conclusion that all possible

>> universes exist.

>>

>>

>> No, it doesn't prove they all exist, just that there are perhaps

>> infinitely many universes almost exactly like this one.

>

>> universes exist.

>>

>>

>> No, it doesn't prove they all exist, just that there are perhaps

>> infinitely many universes almost exactly like this one.

>

> Maybe I'm not understanding what you mean by "independent structures".

> Independent of what? I don't see that referring to independent> structures has anything to do with whether they exist.

>

>> Which, while not proving everything exists, is certainly something we

>> would expect to find if indeed everything exists.

>

> Of course it is trivial to say that an everything theory successfully

> whether it does the converse. Can it predict that we don't see some

> (almost all) things.

>

I'd say that it could. A theory like COMP predicts many possibilities

outside any modern physical theories, some such things are very much

testable, but not falsifiable (because the only way we have of testing

something is by observing it and if we are part of the experiment, that

leads to tricky philosophy of science problems, which can be remedied by

thinking of reality as shared computations by a large population of

observers, not an inescapable 3p reality).

If this world was a Harry Potter magical irreducible universe or

something equally weird like purely Newtonian physics, yet with physical

(non-simulated brain), I would say that could refute COMP. Why? COMP

leads to an increase of possible continuations and so do other

everything-theories. Which essentially means that if such a theory is

true then certain types of experiences are more probable than others,

while others are utterly unlikely (but not impossible). This is yet

another way to test these types of theories.

>>

>> There are all these reasons and arguments that are compatible with and

>> suggestive of the idea that all is out there. I haven't seen one

>> offered piece of evidence from you that would suggest the idea of

>> mathematical reality is false. So tell me: for what reason(s) do you

>> reject the hypothesis?

>

> I don't reject it; I just don't accept it. It seems to ill defined to be

> testable.

>

I find it 'everything' theories more plausible than 'something' theories

- why? Ask the question "why these particlar laws of physics?" or "is

there any reason to suppose only this box in which we happen to be

exists and no other boxes which we have not observed exist?". The

'everything' theory is always simpler by Occam or other heuristics which

prefer theories of reduced complexity. The Jahweh 'theory' has way too

high complexity.

A skeptical person would not believe anything they did not experience,

but then their position would be irrealist or merely instrumental - they

refuse to try and guess what's underneath and only predict by their

experience and nothing more. A realist (but sometimes also monist or

even idealist) position would assume that something is going on

underneath and understand what it is instead of just refusing to ask

that question.

>>

>>> This can also be considered as confirmation of the theory that there

>>> exists a

>>> huge diversity in structures that have existence. Just because one

>>> proposed test

>>> will not work should not imply a theory is untestable.

>>>

>>> A final thought: Consider what our universe would look like if you

>>> were a being

>>> outside it. You would not be affected by the gravity of objects in

>>> our universe,

>>> for gravity only affects physical objects in this universe. You could

>>> not see the

>>> stars or galaxies of our universe, for photons never leave it. There

>>> would be no

>>> relativity of size, or time, or distance between your perspective and

>>> that within

>>> our universe. You could not say what time it happened to be in our

>>> universe, or

>>> whether the world had even formed yet or long ago ended. You could in

>>> no way make

>>> your presence known to us in this universe, for our universe is bound

>>> to follow

>>> certain fixed laws. In summary, outside our universe there is no

>>> evidence we even

>>> exist; our entire universe is merely an abstract, immutable and timeless

>>> mathematical object.

>>

>> That's a complete non sequitur.

>>

>>

>>> From the outside, one could study our universe through the window of

>>> math and

>>> computer simulation,

>>

>> I could study a mathematical or computational representation, but

>> that's not the

>> same as studying our universe - unless you beg the question.

>>

>>

>> Clearly we will not get proof of the mathematical universe hypothesis

>> by seeing other universes and mathematical objects through telescopes.

>> Different universes are independent in such a way that we can only

>> access them as we access all other mathematical structures.

>

> Ask yourself WHY they are inaccessible. Isn't it because if they were

> accessible then there would be contradictory facts in the world. And why

> can't there be contradictory facts? Because ex falso quodlibet. But

> "quodlibet" is what has already been hypothesized. (on the other hand

> see Graham Priest's "In Contradiction").

>

>> Also, if your model is perfect, there should be no difference between

>> studying the model and the object it represents. In the future, we

>> will be able to discover, emulate, and visit other universes by

>> discovering them in math, and using sufficiently powerful simulations,

>> know what it is like there, or whether or not life is possible.

>

> Except if we are studying them or simulating them, then we can interact

> with them and (necessarily?) change them.

>

Changing them means looking at different structure than before - either

at the structure including your changes or the structure in which you're

contained and the inner structure you're simulating.

Interacting with something means they are within the same structure.

Observing merely means simulation or inference.

>>

>> That we cannot affect them from our current location does not make

>> them any less real.

>

> "Affect" and "observe" are two different things (at least classically)

> and if we can neither affect or observe that makes them rather like

> Russell's teapot. We can't be sure it doesn't exist, but there's no

> reason to think it does.

>

There are far better reasons to consider 'everything'-type theories.

Most people don't care about theories about unicorns and ponies, but

they do care about theories about why we exist or why physics behaves

like this or that or why we have this or that experience.

>> That our universe is an immutable, abstract, timeless object to a

>> being in a different universe does not imply we are any less real,

>

> I'm not sure what being "an abstract object to a being" means, but I

> don't think it implies we are any more real.

>

>> that our experiences don't matter, or that the existence of the

>> structure that is our universe is without consequence. Immutability

>> says nothing about an objects reality; we cannot affect the past,

>

> Unless the past was identical with the present then something has mutated.

>

>> or portions of our universe sufficiently far away, yet most would say

>> these exist. Moreover, that other universes are currently inaccessible

>> to us does not necessarily imply that they will always be immutable

>> and inaccessible to us. There is always some non-zero possibility that

>> when you wake up tomorrow, you won't find yourself in this universe,

>> but one very far away.

>

> So you say, but I'm betting not...and so are you.

>

What if you find yourself in a situation which greatly reduces your

measure? I would say that would be grounds for unusual expectations.

There's also a variety of thought experiments (some eventually

realisable as actual experiments) which would let you test at least COMP

or MWI (partially).

>> The existence of all structures reconfirms, in a stronger senses,

>> quantum immortality. If all the other universes are out there, then

>> given mechanism, a we are all immortal. Unlike the immortality implied

>> by quantum immortality, we can even survive destruction of this

>> universe, waking up in a different one where the present one was just

>> a very long dream.

>

> I'm not sure I've survived the past year.

>

I would partially agree with you here (especially with the ending

quote). I don't bet on a very strong continuity myself. I change each

passing moment, and I experience discontinuity while sleeping or

otherwise being unconscious. However, as most humans we have

*expectations* and we unconsciously have such inductive beliefs in a

continuity, and we consciously predict and model some of our

experiences. Some may say that subjective probabilities are a mess and

we shouldn't do them (and thus also ignore UDA/COMP), but I believe in

my own subjective experience (I can't doubt it, although I can see why

eliminativist theories are consistent if we ignore the mind) and I do

know that I care about my future subjective experiences. If you really

want a more precise definition of what 1p-you is, imagine an infinite

directed graph where edges are Observer Moments and this 1p-'you' (or a

history) is like a partial path between 2 points (with some small

length, always losing some of the past and gaining some of the future,

like a fuzzy sliding-window). Taking the disconnected OMs view does not

make as much sense for a creature that cares about their future states

and has mostly correct local expectations (consciously known or not).

> Brent

> The person I was when I was 3 years old is dead. He died because

> too much new information was added to his brain.

> -- Saibal Mitra

>

Mar 6, 2012, 6:22:44 AM3/6/12

to everyth...@googlegroups.com

Stephen,

The life is full of paradoxes. My point was that while philosophers

cannot solve apparently simple problems (well, these problems happen not

to be simple), engineers continue doing their business successfully. How

they do it? I believe, exactly this way, they try to understand what

they do not know. Then they make trials, run tests, etc. and finally

with some luck we get a new technology. Whether the theory of everything

exists or not, happens not be essential for the success in engineering.

I do not know why.

Right now I am at the end of Beweistheorien (Proof Theories) by Prof Hoenen

http://www.podcasts.uni-freiburg.de/podcast_content?id_content=24

At the end of his course, he considers the ontological arguments where

the goal was to proof existence from pure logic. A pretty interesting

attempt. Still there is a huge gap between logic and existence and it

seems that engineers successfully fills it. Ask them, how they do it.

Evgenii

On 05.03.2012 14:34 Stephen P. King said the following:

> On 3/5/2012 7:01 AM, Evgenii Rudnyi wrote:

>> John,

>>

>> It is not that bad to say that we do not know something. Yet, it might

>> be even better to specify more accurately what exactly we do not know.

>>

>> Think of your younger colleagues that do chemistry research right now.

>> Chemists have been quite successful and the story continues. The

>> concepts of atom, molecule, macromolecule, electron density, etc. have

>> helped a lot along this way. We may take this concepts ontologically

>> or just pragmatically, this is after all not that important. Materials

>> science seems not to be affected.

>>

>> Evgenii

...

> Hi Evgenii,

>

> This is a very fascinating statement to me and I find John's comments to

> be very wise! "...it might be even better to specify more accurately

> what exactly we do not know. " Does it not lead to a paradox? For if we

> could state exactly what we do not know then it would be the case that

> we do in fact know it and thus "we would known what we do not know",

> which appears to be a contradiction.

> Is this a sample of a more general kind of situation that is inevitable

> given the idea of self-reference? It seems to me that we need to

> consider that Bivalency

> <http://en.wikipedia.org/wiki/Principle_of_bivalence> can be a source of

Mar 6, 2012, 7:05:24 AM3/6/12

to everyth...@googlegroups.com

What most mathematicians believe is that mathematics are the laws true

in all physical universes. And physics is true in one physical universe.

But with the mechanist hypothesis, we know better: the physical laws

are invariant in all numbers' dreams, and physical universe are shared

computations. This explains also (not directly) the non sharable

truth, the contingent one, etc.

The advantage is that we can explain both quanta and qualia, without

postulating a physical, nor a mental realm, just by listening to the

machine, and not taking them for zombie.

It hurts our intuition, today, but science always do that, since its

claim that the earth is not the center of reality. With comp we can

even understand why science has to hurt machine's intuition.

So a physicalist has just to find non mechanist theory of mind, if we

want the physical universe to be ontological (existing in some primary

sense).

Bruno

Mar 6, 2012, 7:07:14 AM3/6/12

to everyth...@googlegroups.com

Craig,

The danger to society comes not from mathematicians, rather it could

come from technologists. Recently I have read

Jaron Lanier, You Are Not a Gadget: A Manifesto

and the author shows that the society should pay more attention to what

Silicon Valley geeks are silently doing. Just one quote

"Ideals are important in the world of technology, but the mechanism by

which ideals influence events is different than in other spheres of

life. Technologists don't use persuasion to influence you - or, at

least, we don't do it very well. There are a few master communicators

among us (like Steve Jobs), but for the most part we aren't particularly

seductive."

"We make up extensions to your being, like remote eyes and ears

(web-cams and mobile phones) and expanded memory (the world of details

you can search for online). These become the structures by which you

connect to the world and other people. These structures in turn can

change how you conceive of yourself and the world. We tinker with your

philosophy by direct manipulation of your cognitive experience, not

indirectly, through argument. It takes only a tiny group of engineers to

create technology that can shape the entire future of human experience

with incredible speed. Therefore, crucial arguments about the human

relationship with technology should take place between developers and

users before such direct manipulations are designed. This book is about

those arguments."

As for sensations, I do not know. Yesterday after I have read your

email, I went to an Italian restaurant. A small dinner, actually I

wanted just a glass of good red Italian wine, but then I took also a

small plate of cheese assorti with a couple of salad leaves, pepperoni

and bread. I have enjoyed my dinner. Whether wine, bread, cheese, salad

and pepperoni have enjoyed it too, I do not know. I would not mind, if

they did.

Evgenii

On 05.03.2012 06:33 Craig Weinberg said the following:

Mar 6, 2012, 7:26:03 AM3/6/12

to everyth...@googlegroups.com

On 05 Mar 2012, at 19:26, meekerdb wrote:

On 3/5/2012 10:03 AM, Evgenii Rudnyi wrote:On 05.03.2012 18:29 meekerdb said the following:On 3/5/2012 3:23 AM, Evgenii Rudnyi wrote:The experiment takes an operational approach to what Pi means.During the initial stage of the experiment mathematicians prove theexistence of Pi.When mathematicians 'prove the existence' of something they are justshowing that something which satisfies a certain definition can beinferred from a certain set of axioms. In your example themathematicians may define Pi as the ratio of the circumference to thediameter of a circle in Euclidean geometry. But what does that meanif geometry is not Euclidean; and we know it's not since thesemathematicians are in the gravitational field of the Earth.Mathematics is about abstract propositions. Whether they apply toreality is a separate question.BrentI agree that this assumption might not be the best one. I will think it over.However, I do not completely understand you. How the geometry of physical space in which mathematicians reside influences the definition of Pi? Mathematicians will consider just Euclidean geometry, that's it. In my view, whether the physical space Euclidean or not, does not influence the work of mathematicians.

Exactly. Hence mathematics =/= reality.

Right. But this does not prove that reality is not mathematical.

In any case, the problem remains. What is mathematics under the assumption of physicalism? Do you have any idea?

It's a language game.

The word "game" is so fuzzy that this says nothing at all. Game theory is a branch of mathematics.

A physicist goes off to a conference. After a week his suit’s gotten soiled and crumpled, so he goes out to look for a dry cleaner. Walking down the main street of town, he comes upon a store with a lot of signs out front. One of them says “Dry Cleaning.” So he goes in with his dirty suit and asks when he can come back to pick it up. The mathematician who owns the shop replies, “I’m terribly sorry, but we don’t do dry cleaning.” “What?” exclaims the puzzled physicist. “The sign outside says ‘Dry Cleaning’!” “We do not do anything here,” replies the mathematician. “We only sell signs!”

--- Alain Connes, in Changeux

Connes is a mathematical realist. Are you sure the joke is not from Changeux who is strongly physicalist?

Bruno

Mar 6, 2012, 8:21:33 AM3/6/12